Spatiotemporal topological kriging of runoff time series

This paper proposes a geostatistical method for estimating runoff time series in ungauged catchments. The method conceptualizes catchments as space‐time filters and exploits the space‐time correlations of runoff along the stream network topology. We hence term the method topological kriging or top kriging. It accounts for hydrodynamic and geomorphologic dispersion as well as routing and estimates runoff as a weighted average of the observed runoff in neighboring catchments. Top kriging is tested by cross validation on 10 years of hourly runoff data from 376 catchments in Austria and separately for a subset of these data, the Innviertel region. The median Nash‐Sutcliffe efficiency of hourly runoff in the Innviertel region is 0.87 but decreases to 0.75 for the entire data set. For a subset of 208 catchments, the median efficiency of daily runoff estimated by top kriging is 0.87 as compared to 0.67 for estimates of a deterministic runoff model that uses regionalized model parameters. The much better performance of top kriging is because it avoids rainfall data errors and avoids the parameter identifiability issues of traditional runoff models. The analyses indicate that the kriging variance can be used for identifying catchments with potentially poor estimates. The Innviertel region is used to examine the kriging weights for nested and nonnested catchments and to compare various variants of top kriging. The spatial kriging variant generally performs better than the more complex spatiotemporal kriging and spatiotemporal cokriging variants. It is argued that top kriging may be preferable to deterministic runoff models for estimating runoff time series in ungauged catchments, provided stream gauge density is high and there is no need to account for causal rainfall‐runoff processes. Potential applications include the estimation of flow duration curves in a region and near–real time mapping of runoff.